WASHINGTON (AP) -- Religious and cultural conservatives, a political force skeptical of the leading Republican presidential candidates, are caught in a tug of war between pragmatism and ideology.

"My head and my heart are fighting with each other," said Phil Burress, an Ohioan who has lobbied hard for federal and state bans on gay marriage.

The vexing choices facing these voters:

Rudy Giuliani, a thrice-married New Yorker who differs with them on abortion, gays and guns but who polls show offers a strong chance to beat a Democrat next fall.

Mitt Romney, a Mormon from Massachusetts who didn't entirely share their views in the past but who insists he now does.

Fred Thompson, a Tennessean who has not been a vocal champion of their core issues but who had a right-leaning Senate voting record.

John McCain, an Arizona senator who has a clear socially conservative resume but who dismissed their leaders "agents of intolerance" in 2000.

Mike Huckabee, a Southern Baptist minister and true believer who has an extraordinary hill to climb for the nomination.

For now, social-issue conservatives are scattered across the field of candidates.

It's a splintering that is, perhaps, more severe than in previous presidential elections and that raises questions about the power of a long-influential part of the GOP base. The restiveness has prompted talk of a possible third-party bid, a certain political death knell for the GOP nominee.

Reflecting the quandary these voters face, Focus on the Family's James Dobson has rejected Giuliani and has panned both McCain and Thompson. Romney is the only leading candidate Dobson hasn't denounced - but he hasn't publicly backed Romney either.

"There's no one Republican presidential candidate that inspires them, and the movement leaders can find fault in one way or another with all the candidates," said John Green, a senior fellow at the Pew Forum on Religion and Public Life. "It's hard to tell if it means that their influence is waning. But they're likely to have more influence if they stay united. The longer they stay behind several candidates, the less influence they'll have."

While the ultimate impact of these religious and cultural conservatives on the GOP nomination race is anyone's guess, there's no question that they are a force in numbers.

A recent Pew Research Center survey found that 43 percent of Republicans say social issues will be very important in deciding how to vote in 2008, and another 31 percent call issues like abortion and marriage somewhat important.

Associated Press-Ipsos polls show that nearly two-thirds of Republicans consider themselves conservative, with Thompson and Giuliani getting about equal support from that group while McCain and Romney trail.

Roughly one in five conservatives, churchgoers and Christian evangelicals are undecided.

Thompson has a slight edge over Giuliani among the half of all Republicans who attend weekly religious services as well as among those who call themselves born-again Christians. McCain and Romney lag in both categories.

The White House hopefuls will make their pitches this weekend to a few thousand "values voters" gathering in Washington for a summit sponsored by the Family Research Council, a conservative advocacy group.

Uncertainty about a consensus candidate - and anxiety over the possibility of nominating Giuliani - serves as a backdrop.

"Our heads are telling us that we've got to settle for someone that can win even if he's not the closest to our values. I've decided that I can't do that. I've got to go with my heart," said Burress, who says he's leaning toward Huckabee but has not committed.

Some fear that if they stay divided as a group, their power will be diluted and they will, in effect, be handing the nomination to the antithesis of what they believe - Giuliani.

"We have to reconcile the tension between pure principle and pure pragmatism," said John Stemberger, an Orlando lawyer and a leading social conservative in Florida who says he has not chosen a candidate. "If we vote on pure principle, we forfeit the opportunity to influence policy through politics. If we vote on pure pragmatism, then we sell our souls to the man."

Some are trying to see a silver lining in the lack of a favored candidate.

"It's important to have our people in as many different campaigns as possible so our issues aren't lost," said Kelly Shackelford, president of the Free Market Foundation in Texas who isn't backing any one person yet.

As the summit opens, attendees will watch for the fallout from several recent developments:

Influential social conservative leaders met privately in Salt Lake City to weigh their options if Giuliani wins the nomination. They overwhelmingly approved a resolution pledging to support a minor-party candidate if the Democratic and Republican nominees back abortion rights, and discussed possibly creating a third party. The group meets again Saturday in Washington.

Giuliani, the former New York mayor who backs abortion and gay rights, won the support of two anti-abortion Republicans, including Texas Gov. Rick Perry. Romney, who once backed abortion rights but has reversed himself, earned the endorsement of Bob Jones III, the chancellor of a Christian fundamentalist school in South Carolina.

Thompson entered the race late and, thus far, has failed to emerge as the conservative white knight his backers had promised. He posted an advertisement on conservative Web sites this week criticizing Romney and Giuliani on values issues. "Fred Thompson. The REAL Conservative," it declares.

Sen. Sam Brownback of Kansas, a darling of the religious right, decided to drop out of the race after his campaign failed to catch on. That leaves his supporters searching for a candidate, and at least two competitors, Huckabee and McCain, hoping for Brownback's endorsement.

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